PERTH, Australia — Authorities are confident that signals detected deep in the Indian Ocean are from the missing Malaysian jet’s black boxes, Australia’s prime minister said Friday, raising hopes they are near solving one of aviation’s most perplexing mysteries.

Tony Abbott told reporters in Shanghai that crews hunting for Flight 370 have zeroed in on a more targeted area in their search for the source of the sounds, first heard on Saturday.

‘‘We have very much narrowed down the search area and we are very confident that the signals that we are detecting are from the black box on MH370,’’ Abbott said.

‘‘Nevertheless, we’re getting into the stage where the signal from what we are very confident is the black box is starting to fade,’’ he added. ‘‘We are hoping to get as much information as we can before the signal finally expires.’’

The plane’s black boxes, or flight data and cockpit voice recorders, may hold the answers to why the Boeing 777 lost communications and veered so far off course when it vanished March 8 while flying from Kuala Lumpur, Malaysia, to Beijing with 239 people on board.

Search crews are racing against time because the batteries powering the devices’ locator beacons last only about a month — and more than a month has passed since the plane disappeared. Finding the black boxes after the batteries fail will be extremely difficult because the water in the area is 4,500 meters (15,000 feet) deep.

The Australian ship Ocean Shield is towing a U.S. Navy device that detects black box signals, and two sounds it heard Saturday were determined to be consistent with the signals emitted from aircraft flight recorders. Two more sounds were detected in the same general area on Tuesday.

‘‘We are confident that we know the position of the black box flight recorder to within some kilometers,’’ Abbott said. ‘‘But confidence in the approximate position of the black box is not the same as recovering wreckage from almost 4 ½ kilometers beneath the sea or finally determining all that happened on that flight.’’

An Australian air force P-3 Orion, which has been dropping sonar buoys into the water near where the Ocean Shield picked up the sounds, detected another possible signal on Thursday, but Angus Houston, who is coordinating the search for Flight 370, said in a statement that an initial assessment had determined it was not related to an aircraft black box.

The buoys each have a hydrophone listening device that dangles about 300 meters (1,000 feet) below the surface and their data is sent via radio back to a plane, Royal Australian Navy Commodore Peter Leavy said.

The Ocean Shield was still towing its pinger locator to try to find additional signals on Friday, and the Orions were continuing their hunt, Houston said. The underwater search zone is currently a 1,300-square-kilometer (500-square-mile) patch of the ocean floor, about the size of the city of Los Angeles.

‘‘It is vital to glean as much information as possible while the batteries on the underwater locator beacons may still be active,’’ Houston said in a statement.

The searchers are trying to pinpoint the exact location of the source of the signals so they can send down a robotic submersible to look for wreckage. Houston said on Friday that a decision to send the sub could be ‘‘some days away.’’

The Bluefin 21 submersible takes six times longer to cover the same area as the pinger locator being towed by the Ocean Shield and would take six weeks to two months to canvass the current underwater search zone.

Complicating matters is the depth of the seabed in the search area. The signals are emanating from 4,500 meters (15,000 feet) below the surface, which is the deepest the Bluefin can dive. The search coordination center said it was considering options in case a deeper-diving sub is needed.

Meanwhile, the center said the surface area to be searched for floating debris had been narrowed to 46,713 square kilometers (18,036 square miles) of ocean extending from 2,300 kilometers (1,400 miles) northwest of Perth. Up to 15 planes and 13 ships were conducting the visual search Friday, west of the underwater search based on expected drift from the suspected crash site.

Investigators believe the plane went down in the southern Indian Ocean based on a flight path calculated from its contacts with a satellite and analysis of its speed and fuel capacity.

Separately, a Malaysian government official said Thursday that investigators have concluded the pilot spoke the last words to air traffic control, ‘‘Good night, Malaysian three-seven-zero,’’ and that his voice had no signs of duress. A re-examination of the last communication from the cockpit was initiated after authorities last week reversed their initial statement that the co-pilot was speaking different words.

The senior government official spoke on condition of anonymity because he wasn’t authorized to speak to the media.